In this thesis channel capacity of a special type of multiple-input multiple-output (MIMO) Rayleigh fading channels is studied, where the transmitters are subject to a finite phase-shift keying (PSK) input alphabet. The constraint on the input alphabet makes an analytical solution for the capacity beyond reach. However we are able to simplify the final expression, which requires a single expectation and thus can be evaluated easily through simulation. To facilitate simulations, analytical expressions are derived for the eigenvalues and eigenvectors of a covariance matrix involved in the simplified capacity expression. The simplified expression is used to provide some good approximations to the capacity at low signal-to-noise ratios (SNRs). Involved in derivation of the capacity is the capacity-achieving input distribution. It is proved that a uniform prior distribution is capacity achieving. We also show that it is the only capacity-achieving distribution for our channel model. On top of that we generalize the uniqueness case for an input distribution to a broader range of channels.